Code_Aster
®
Version
7.4
Titrate:
HSLA303 - Roll under pressure and thermal dilation
Date:
25/11/05
Author (S):
X. DESROCHES
Key
:
V7.12.303-A
Page:
1/6
Manual of Validation
V7.12 booklet: - HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.12 booklet: -
Document: V7.12.303
HSLA303 - Roll under pressure and dilation
thermics
Summary:
Calculation is carried out into axisymmetric. The goal of the test is to validate the initial deformations (key word
EPSI_INIT).
The cylinder is subjected to a homogeneous thermal dilation (
T constant).
The followed procedure is as follows:
·
that is to say
1 the field of deformations resulting from one 1
Er
calculation, the cylinder being subjected to a dilation
homogeneous thermics
T (U
1
the field of resulting displacements),
·
in the second calculation, the cylinder is subjected to an internal pressure, with like deformations
initial the field of deformations
1 (either U
2
the resulting field of displacements),
·
one then compares the results with the field U, obtained with cylinder under pressure, but without
initial deformations. One must have the relation: U
2
= U + U
1
.
Code_Aster
®
Version
7.4
Titrate:
HSLA303 - Roll under pressure and thermal dilation
Date:
25/11/05
Author (S):
X. DESROCHES
Key
:
V7.12.303-A
Page:
2/6
Manual of Validation
V7.12 booklet: - HT-66/05/005/A
1
Problem of reference
1.1 Geometry
Length:
L
= 1 m
Thickness:
H
= 0.0025 m
External radius:
Re = 0.05 m
1.2
Material properties
E = 2.1 X 10
11
AP
v
= 0.3
= 0.12 X 10
- 4
/°C
1.3
Boundary conditions and loadings
·
Section AB in support (direction Z),
·
Thermal dilation in the thickness (calculation 1):
T = 100°C
·
Internal pressure (calculation 2): p = 2 X 10
8
NR/m
2
·
Taking into account of the basic effect.
1.4 Conditions
initial
Without object for the static analysis.
R
L
C
D
Z
H
O
With
B
Code_Aster
®
Version
7.4
Titrate:
HSLA303 - Roll under pressure and thermal dilation
Date:
25/11/05
Author (S):
X. DESROCHES
Key
:
V7.12.303-A
Page:
3/6
Manual of Validation
V7.12 booklet: - HT-66/05/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
·
The deformation due to direct compression is given by:
zz
E
v
R
H
Eh
p
=
-
-
=
(
) (
)
1 2
2
4
3.714 X 10
- 3
, Re = external radius
·
Axial displacement due to the pressure is given by:
U
Z
= Z
zz
·
The deformations due to the thermal loading are worth:
rr
Z Z
T
=
=
=
=
1.2 X 10
- 3
·
Radial displacement due to the thermal loading is worth:
U
R
R
=
rr
=
1.2 X 10
- 3
R
2.2
Results of reference
·
Deformation and radial and axial displacement at the points A, B, C, D due to the thermal loading.
·
Deformation and axial displacement at the points A, B, C, D due to the pressure.
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
7.4
Titrate:
HSLA303 - Roll under pressure and thermal dilation
Date:
25/11/05
Author (S):
X. DESROCHES
Key
:
V7.12.303-A
Page:
4/6
Manual of Validation
V7.12 booklet: - HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
AXIS, mesh Q 8
Cutting:
10 elements according to the length
1 element in the thickness
Limiting conditions:
in A, B
DDL_IMPO = (GROUP_NO = “A”, DY = 0. )
DDL_IMPO = (GROUP_NO = “B”, DY = 0. )
Pressure + basic effect: field U
PRES_REP:
(GROUP_MA = cont_pr, CLOSE = 2.E8)
FORCE_CONTOUR: (GROUP_MA = effond, FY = 1.95E9)
Thermal dilation: U1 field
char_no:
CREA_CHAMP
(AFFE = (ALL = “YES”, NOM_CMP = “TEMP”, VALE = 100.) )
char_th:
AFFE_CHAR_MECA
(TEMP_CALCULEE = char_no)
Initial deformations: U2 field
EPSI_INIT:
(ALL = “YES”, EPXX = 1.2E-3, EPYY = 1.2E-3,
EPZZ = 1.2E-3, EPXY = 0.)
Names of the nodes:
With = N1
B = N2
C = N3
D = N4
3.2
Characteristics of the mesh
A number of nodes: 53
A number of meshs and types: 10 QUAD8, 22 SEG3
3.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE
“AXIS”
ALL
AFFE_CHAR_MECA DDL_IMPO
TEMP_CALCULEE
PRES_REP
GROUP_NO
GROUP_MA
CREA_CHAMP AFFE
CALC_CHAM_ELEM OPTION
“EPSI_ELNO_DEPL”
AFFE_CHAR_MECA EPSI_INIT
Code_Aster
®
Version
7.4
Titrate:
HSLA303 - Roll under pressure and thermal dilation
Date:
25/11/05
Author (S):
X. DESROCHES
Key
:
V7.12.303-A
Page:
5/6
Manual of Validation
V7.12 booklet: - HT-66/05/005/A
4
Results of modeling A
4.1 Values
tested
Results concerning the fields U
1
, U
2
, U
Field Localization Variables Reference Aster
% Reference
Field
U1 thermics
In Ur (DX)
5.7 X 10
- 5
5.7 X 10
- 5
- 6.42 X 10
- 11
B
Ur
(DX)
6 X 10
- 5
6 X 10
- 5
- 7.14 X 10
- 11
C
Ur (DX)
6 X 10
- 5
6 X 10
- 5
8.29 X 10
- 12
DY
1.2 X 10
- 3
1.2 X 10
- 3
3.9 X 10
- 10
D
Ur (DX)
5.7 X 10
- 5
5.7 X 10
- 5
1.19 X 10
- 11
U (DY)
1.2 X 10
- 3
1.2 X 10
- 3
3.9 X 10
- 10
With, M1 mesh
rr
1.2 X 10
- 3
1.2 X 10
- 3
- 1.91 X 10
- 10
1.2 X 10
- 3
1.2 X 10
- 3
5.54 X 10
- 10
zz
1.2 X 10
- 3
1.2 X 10
- 3
- 1.12 X 10
- 10
B, M1 mesh
rr
1.2 X 10
- 3
1.2 X 10
- 3
- 1.89 X 10
- 10
1.2 X 10
- 3
1.2 X 10
- 3
5.57 X 10
- 10
zz
1.2 X 10
- 3
1.2 X 10
- 3
- 1.16 X 10
- 10
C, M10 mesh
rr
1.2 X 10
- 3
1.2 X 10
- 3
- 3.74 X 10
- 11
1.2 X 10
- 3
1.2 X 10
- 3
1.08 X 10
- 10
zz
1.2 X 10
- 3
1.2 X 10
- 3
- 4.74 X 10
- 12
D, M10 mesh
rr
1.2 X 10
- 3
1.2 X 10
- 3
- 3.98 X 10
- 11
1.2 X 10
- 3
1.2 X 10
- 3
1.12 X 10
- 10
zz
1.2 X 10
- 3
1.2 X 10
- 3
- 2.93
x10
- 12
Field of
pressure U
C
U
(DY)
3.714 X 10
- 3
3.997 X 10
- 3
7.614
D
U
(DY)
3.714 X 10
- 3
3.997 X 10
- 3
7.614
C, M10 mesh
3.714 X 10
- 3
3.996 X 10
- 3
7.602
D, M10 mesh
3.714 X 10
- 3
3.996 X 10
- 3
7.602
U2 field
C
U
4.914 X 10
- 3
5.197 X 10
- 3
5.754
D
U
4.914 X 10
- 3
5.197 X 10
- 3
5.754
C,
net
4.914 X 10
- 3
5.196 X 10
- 3
5.746
D,
net
4.914 X 10
- 3
5.196 X 10
- 3
5.746
4.2 Remarks
·
The goal of the test is not to obtain a high degree of accuracy on the level of the results, but simply
to check the relation: U
2
= U + U
1
; so calculation was carried out only with one mesh
coarse.
·
It is noted that the required relation is well checked at the loose lead of the cylinder.
·
It is checked in addition that the field of deformation resulting from thermal dilation is
uniformly equal to 1.2 X 10
- 3
.
Code_Aster
®
Version
7.4
Titrate:
HSLA303 - Roll under pressure and thermal dilation
Date:
25/11/05
Author (S):
X. DESROCHES
Key
:
V7.12.303-A
Page:
6/6
Manual of Validation
V7.12 booklet: - HT-66/05/005/A
5
Summary of the results
Option EPSI_INIT (initial deformations into constant) provides completely satisfactory results.